The Computational Complexity of Learning Gaussian Single-Index Models

arXiv:2403.05529v1 Announce Type: new
Abstract: Single-Index Models are high-dimensional regression problems with planted structure, whereby labels depend on an unknown one-dimensional projection of the input via a generic, non-linear, and potentially non-deterministic transformation. As such, they encompass a broad class of statistical inference tasks, and provide a rich template to study statistical and computational trade-offs in the high-dimensional regime.
While the information-theoretic sample complexity to recover the hidden direction is linear in the dimension $d$, we show that computationally efficient …

abstract arxiv class complexity computational cs.lg index inference labels linear non-linear projection regression statistical stat.ml study tasks template transformation type via